Learned Sorted Table Search and Static Indexes in Small Space: Methodological and Practical Insights via an Experimental Study

Sorted Table Search Procedures are the quintessential query-answering tool, still very useful, e.g, Search Engines (Google Chrome). Speeding them up, in small additional space with respect to the table being searched into, is still a quite significant achievement. Static Learned Indexes have been very successful in achieving such a speed-up, but leave open a major question: To what extent one can enjoy the speed-up of Learned Indexes while using constant or nearly constant additional space. By generalizing the experimental methodology of a recent benchmarking study on Learned Indexes, we shed light on this question, by considering two scenarios. The first, quite elementary, i.e., textbook code, and the second using advanced Learned Indexing algorithms and the supporting sophisticated software platforms. Although in both cases one would expect a positive answer, its achievement is not as simple as it seems. Indeed, our extensive set of experiments reveal a complex relationship between query time and model space. The findings regarding this relationship and the corresponding quantitative estimates, across memory levels, can be of interest to algorithm designers and of use to practitioners as well. As an essential part of our research, we introduce two new models that are of interest in their own right. The first is a constant space model that can be seen as a generalization of $k$-ary search, while the second is a synoptic {\bf RMI}, in which we can control model space usage.